And-or graphs and theorem-proving graphs determine the same kind of search space and differ only in the direction of search: from axioms to goals, in the case of theorem-proving graphs, and in the opposite direction, from goals to axioms, in the case of and-or graphs. We investigate the construction of a single general algorithm which covers unidirectional search both for and-or graphs and for theorem-proving graphs, bidirectional search for path-finding problems and search for a simplest solution as well as search for any solution. Indeed, many different search spaces can represent the same original problem, as in the case of resolution systems where different refinements of the resolution rule determine different search spaces for a single problem of demonstrating the unsatisfiability of a given set of clauses. In the tree representation of theorem-proving graphs (used in Machine Intelligence 5 (Kowalski 1969)), identical problems Tare generated at different times, working forwards from the initial set of axioms {D, E, F, G}.

In designing an actual realization of the unification algorithm the first question which arises is how best to represent the expressions in the computer store. We have a collection of tables: symbol, args, vble, arity, subst, term, equals, and part, each of which has the same number N of rows. All the tables have one column, with the exception of args; and args has as many columns as the arity of that symbol, in the expressions being represented, whose arity is largest. We always arrange matters so that in a normal representation, distinct rows represent distinct expressions, i.e., so that We are now ready to explain the computation.

This thesis is concerned with algorithms for generating generalisations-from experience. These algorithms are viewed as examples of the general concept of a hypothesis discovery system which, in its turn, is placed in a framework in which it is seen as one component in a multi-stage process which includes stages of hypothesis criticism or justification, data gathering and analysis and prediction. Formal and informal criteria, which should be satisfied by the discovered hypotheses are given. In particular, they should explain experience and be simple. The formal work uses the first-order predicate calculus. These criteria are applied to the case of hypotheses which are generalisations from experience. A formal definition of generalisation from experience, relative to a body of knowledge is developed and several syntactical simplicity measures are defined. This work uses many concepts taken from resolution theory (Robinson, 1965). We develop a set of formal criteria that must be satisfied by any hypothesis generated by an algorithm for producing generalisation from experience. The mathematics of generalisation is developed. In particular, in the case when there is no body of knowledge, it is shown that there is always a least general generalisation of any two clauses, in the generalisation ordering. (In resolution theory, a clause is an abbreviation for a disjunction of literals.) This least general generalisation is effectively obtainable. Some lattices induced by the generalisation ordering, in the case where there is no body of knowledge, are investigated. The formal set of criteria is investigated. It is shown that for a certain simplicity measure, and under the assumption that there is no body of knowledge, there always exist hypotheses which satisfy them. Generally, however, there is no algorithm which, given the sentences describing experience, will produce as output a hypothesis satisfying the formal criteria. These results persist for a wide range of other simplicity measures. However several useful cases for which algorithms are available are described, as are some general properties of the set of hypotheses which satisfy the criteria. Some connections with philosophy are discussed. It is shown that, with sufficiently large experience, in some cases, any hypothesis which satisfies the formal criteria is acceptable in the sense of Hintikka and Hilpinen (1966). The role of simplicity is further discussed. Some practical difficulties which arise because of Goodman's (1965) "grue" paradox of confirmation theory are presented. A variant of the formal criteria suggested by the work of Meltzer (1970) is discussed. This allows an effective method to be developed when this was not possible before. However, the possibility is countenanced that inconsistent hypotheses might be proposed by the discovery algorithm. The positive results on the existence of hypotheses satisfying the formal criteria are extended to include some simple types of knowledge. It is shown that they cannot be extended much further without changing the underlying simplicity ordering. A program which implements one of the decidable cases is described. It is used to find definitions in the game of noughts and crosses and in family relationships. An abstract study is made of the progression of hypothesis discovery methods through time. Some possible and some impossible behaviours of such methods are demonstrated. This work is an extension of that of Gold (1967) and Feldman (1970). The results are applied to the case of machines that discover generalisations. They are found to be markedly sensitive to the underlying simplicity ordering employed. Ph.D. thesis, Edinburgh University.

A general game-playing program must know the rules of the particular playing game. These rules are:(1) an algorithm indicating the winning state;(2) an algorithm enumerating legal moves. A move gives a set of changes from the present situation.There are two means of giving these rules:(1) We can write a subroutine which recognizes if we have won and another which enumerates legal moves. Such a subroutine is a black box giving to the calling program the answer: 'you win' or 'you do not win', or the list of legal moves. But it cannot know what is in that subroutine.(2) We can also define a language in which we describe the rules of a game. The program investigates the rules written with this language and finds some indications to improve its play. Artificial Intelligence and Heuristic Programming Edinburgh University Press

Ph.D. dissertation "Bi-directional and heuristic search in path problems" (Stanford, Computer Science, 1970) summarized in this article in Machine Intelligence 6 (1971).In the uni-directional algorithms, the search proceeds from an initial nodeforward until the goal node is encountered. Problems for which the goal nodeis explicitly known can be searched backward from the goal node. Analgorithm combining both search directions is bi-directional.This method has not seen much use because book-keeping problems werethought to outweigh the possible search reduction. The use of hashingfunctions to partition the search space provides a solution to some of theseimplementation problems. However, a more serious difficulty is involved.To realize significant savings in bi-directional search, the forward andbackward search trees must meet in the 'middle' of the space. The potentialbenefits from this technique motivates this paper's examination of thetheoretical and practical problems in using bi-directional search.

Such a program receives as data the rules of a game: an algorithm enumerating the moves and an algorithm indicating how to win. We describe the part of the program playing the combinatorial game in order to win: how it can find the moves which lead to victory and what are the only opponent's moves with which he does not lose. The man in square A becomes a new type T. To sum up, the rules of a game are given as algorithms written in the language described above: an algorithm enumerating legal moves and an algorithm indicating how to win. If we play qi, the opponent must prevent us from playing M or destroy one of the conditions already fulfilled; he must destroy one of the Ci to prevent us from playing M next, which thus enables us to win, or one of the Ei or k1 to destroy a condition already fulfilled.

This paper is a survey of the current machine translation research in the US, Europe and Japan. A short history of machine translation is presented first, followed by an overview of the current research work. Representative examples of a wide range of different approaches adopted by machine translation researchers are presented. In support of this discussion, issues in, and techniques for, evaluating machine translation systems are addressed.

In brief, we believe that programs for learning large games will need to have at their disposal good rules for learning small games. Each separate box functions as a separate learning machine: it is only brought into play when the corresponding board position arises, and its sole task is to arrive at a good choice of move for that specific position. The demon's task is to make his choices in successive plays in such a way as to maximise his expected number of wins over some specified period. By a development of Laplace's Law of Succession we can determine the probability, This defines the score associated with the node N. To make a move the automaton examines all the legal alternatives and chooses the move leading to the position having the highest associated score, ties being decided by a random choice.

Aizerman, M. | Braverman, E. | Rozonoer, L.

This article presents a design principle of a neural network using Gaussian activation functions, referred to as a Gaussian Potential Function Network (GPFN), and explores the capability of a GPFN in learning a continuous input-output mapping from a given set of teaching patterns. The design principle is highlighted by a Hierarchically Self-Organizing Learning (HSOL) algorithm featuring the automatic recruitment of hidden units under the paradigm of hierarchical learning. A GPFN generates an arbitrary shape of a potential field over the domain of the input space, as an input-output mapping, by synthesizing a number of Gaussian potential functions provided by individual hidden units referred to as Gaussian Potential Function Units (GPFUs). Simulations were conducted for the demonstration and evaluation of the GPFNs constructed based on the HSOL algorithm for several sets of teaching patterns.